【摘 要】
：
2002年全国高中数学联赛二试第二题如下: 实数a,b,c和正数λ使得f(x)=x~3+ax~2+bx+c有三个实根x_1,x_2,x_3,且满足(1)x_2-x_1=λ;(2)x_3>(1/2)(x_1+x_2),求(2a~3+27c-9ab)/
【机 构】
：
浙江杭州中国计量学院 310034
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2002年全国高中数学联赛二试第二题如下: 实数a,b,c和正数λ使得f(x)=x~3+ax~2+bx+c有三个实根x_1,x_2,x_3,且满足(1)x_2-x_1=λ;(2)x_3>(1/2)(x_1+x_2),求(2a~3+27c-9ab)/λ~3的最大值. 标准答案计算较繁,思路隐晦曲折,不易想到,今给出更直接更简单的解法.
The second question of the 2002 National High School Mathematics League Second Test is as follows: The real numbers a, b, c and the positive number λ make f(x) = x~3+ax~2+bx+c have three real roots x_1, x_2, x_3, and Satisfy (1) x_2-x_1=λ; (2)x_3>(1/2)(x_1+x_2), find the maximum of (2a~3+27c-9ab)/λ~3. The idea is hidden and twisted, and it is hard to think of it. This gives a more direct and simpler solution.
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